Analytics and Modeling

This knowledge area embodies a variety of data driven analytics, geocomputational methods, simulation and model driven approaches designed to study complex spatial-temporal problems, develop insights into characteristics of geospatial data sets, create and test geospatial process models, and construct knowledge of the behavior of geographically-explicit and dynamic processes and their patterns.

Topics in this Knowledge Area are listed thematically below. Existing topics are in regular font and linked directly to their original entries (published in 2006; these contain only Learning Objectives). Entries that have been updated and expanded are in bold. Forthcoming, future topics are italicized. 

 

Conceptual Frameworks for Spatial Analysis & Modeling Data Exploration & Spatial Statistics Network & Location Analysis
Basic Primitives Spatial Sampling for Spatial Analysis Intro to Network & Location Analysis
Spatial Relationships Exploratory Spatial Data Analysis (ESDA) Network Route & Tour Problems
Neighborhoods Kernels & Density Estimation Location & Service Area Problems
First & Second Laws of Geography Spatial Interaction Modelling Accessibility
Spatial Statistics Cartographic Modeling Location-allocation Modeling
Methodological Context Multi-criteria Evaluation The Classic Transportation Problem
Spatial Analysis as a Process Spatial Process Models Space-Time Analysis & Modeling
Geospatial Analysis & Model Building Grid-based Statistics and Metrics Time Geography
Changing Context of GIScience Landscape Metrics Capturing Spatio-Temporal Dynamics in Computational Modeling 
Data Manipulation DEM and Terrain Metrics GIS-Based Computational Modeling
Point, Line, and Area Generalization Point Pattern Analysis Computational Movement Analysis
Coordinate transformations Classification & Clustering Accounting for Errors in Space-Time Modeling
Data conversion Global Measures of Spatial Association Geocomputational Methods & Models
Impacts of transformations Local Measures of Spatial Association Cellular Automata
Raster resampling Simple Regression & Trend Surface Analysis Agent-based Modeling
Vector-to-raster and raster-to-vector conversions Geographically Weighted Regression Simulation Modeling
Generalization & Aggregation Spatial Autoregressive & Bayesian Methods Simulation & Modeling Systems for Agent-based Modeling
Transaction Management Spatial Filtering Models Artificial Neural Networks
Building Blocks   Genetic Algorithms & Evolutionary Computing 
Spatial & Spatiotemporal Data Models Surface & Field Analysis Big Data & Geospatial Analysis
Length & Area Operations Modeling Surfaces Problems & with Large Spatial Databases
Polyline & Polygon Operations Surface Geometry Pattern Recognition & Matching
Overlay & Combination Operations Intervisibility Artificial Intelligence Approaches
Areal Interpolation Watersheds & Drainage Data Mining Approaches
Classification & Clustering Gridding, Interpolation, and Contouring Rule Learning for Spatial Data Mining
Boundaries & Zone Membership Deterministic Interpolation Models Machine Learning Approaches
Tesselations & Triangulations Inverse Distance Weighting CyberGIS
Spatial Queries Radial Basis & Spline Functions Analysis of Errors & Uncertainty
Distance Operations Triangulation Problems of Currency, Source, and Scale
Buffers Polynomial Functions Problems of Scale & Zoning
Directional Operations Core Concepts in Geostatistics Theory of Error Propagation
Grid Operations & Map Algebra Kriging Interpolation Propagation of Error in Geospatial Modeling
    Fuzzy Aggregation Operators
    Mathematical Models of Uncertainty

 

AM-32 - Spatial autoregressive models
  • Explain Anselin’s typology of spatial autoregressive models
  • Demonstrate how the parameters of spatial auto-regressive models can be estimated using univariate and bivariate optimization algorithms for maximizing the likelihood function
  • Justify the choice of a particular spatial autoregressive model for a given application
  • Implement a maximum likelihood estimation procedure for determining key spatial econometric parameters
  • Apply spatial statistic software (e.g., GEODA) to create and estimate an autoregressive model
  • Conduct a spatial econometric analysis to test for spatial dependence in the residuals from least-squares models and spatial autoregressive models
AM-34 - Spatial expansion and geographically weighted regression
  • Perform an analysis using the geographically weighted regression technique
  • Discuss the appropriateness of GWR under various conditions
  • Describe the characteristics of the spatial expansion method
  • Explain the principles of geographically weighted regression
  • Compare and contrast GWR with universal kriging using moving neighborhoods
  • Explain how allowing the parameters of the model to vary with the spatial location of the sample data can be used to accommodate spatial heterogeneity
  • Analyze the number of degrees of freedom in GWR analyses and discuss any possible difficulties with the method based on your results
AM-33 - Spatial filtering
  • Identify modeling situations where spatial filtering might not be appropriate
  • Demonstrate how spatial autocorrelation can be “removed” by resampling
  • Explain how dissolving clusters of blocks with similar values may resolve the spatial correlation problem
  • Explain how the Getis and Tiefelsdorf-Griffith spatial filtering techniques incorporate spatial component variables into OLS regression analysis in order to remedy misspecification and the problem of spatially auto-correlated residuals
  • Explain how spatial correlation can result as a side effect of the spatial aggregation in a given dataset
  • Describe the relationship between factorial kriging and spatial filtering
AM-10 - Spatial Interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.
 

AM-14 - Spatial process models
  • Discuss the relationship between spatial processes and spatial patterns
  • Differentiate between deterministic and stochastic spatial process models
  • Describe a simple process model that would generate a given set of spatial patterns
AM-26 - Spatial sampling for statistical analysis
  • List and describe several spatial sampling schemes and evaluate each one for specific applications
  • Differentiate between model-based and design-based sampling schemes
  • Design a sampling scheme that will help detect when space-time clusters of events occur
  • Create spatial samples under a variety of requirements, such as coverage, randomness, and transects
  • Describe sampling schemes for accurately estimating the mean of a spatial data set
AM-42 - The Classic Transportation Problem

The classic transportation problem concerns minimizing the cost of transporting a single product from sources to destinations. It is a network-flow problem that arises in industrial logistics and is considered as a special case of linear programming. The total number of units produced at each source, the total number of units required at each destination and the cost to transport one unit from each source to each destination are the basic inputs. The objective is to minimize the total cost of transporting the units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and 3) improving the current solution through iteration. Modeling and solving the classic transportation problem rely strongly on network models, least-cost path algorithms, and location-allocation analysis in the field of geographic information science (GIScience). Thus, it represents a key component in the network analytics and modeling area of GIS&T.

AM-86 - Theory of error propagation
  • Describe stochastic error models
  • Exemplify stochastic error models used in GIScience
AM-59 - Vector-to-raster and raster-to-vector conversions
  • Explain how the vector/raster/vector conversion process of graphic images and algorithms takes place and how the results are achieved
  • Create estimated tessellated data sets from point samples or isolines using interpolation operations that are appropriate to the specific situation
  • Illustrate the impact of vector/raster/vector conversions on the quality of a dataset
  • Convert vector data to raster format and back using GIS software
AM-89 - Weighting schemes
  • Evaluate a fuzzy weighting scheme in terms of uncertainty and error propagation

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